Aging in a mean field elastoplastic model of amorphous solids

Abstract

Note: This paper is part of the Special Topic, Dynamics of Out-of-Equilibrium Soft Materials.

Scaling description of creep flow in amorphous solids

“…Usual mean-field approaches, both for the yielding transition in amorphous solids [32,34] and for the de-pinning transition [35], consider the dynamics of the distribution P (x), where x is a local variable indicating how much additional shear stress is required to have a plastic event. In such models, γ(t) following some initial condition was computed at Σ = 0 and T = 0 [36,37]. These results are consistent with our prediction for ν, supporting that our assumption of analyticity is equivalent to mean-field approaches as is the case in Landau theory.…”

“…In that case, the fluidisation time is likely controlled by the nucleation of a narrow shear band, whose mechanism is debated [7][8][9]. (a) Experimentally measured creep flow in carbopol microgel [11] at imposed stress values of (from bottom to top: σ[Pa] = 35,36,37,38,40,43,45,50,55,60). At higher imposed stresses, creep flow eventually undergoes fluidisation while it arrests at lower stresses (the lowest two in this case).…”

Yielding behavior of glasses under asymmetric cyclic deformation

“…Recent years have witnessed significant activity in developing a statistical mechanical description of these phenomena [2][3][4][5]. Yielding behaviour in model amorphous solids has been investigated experimentally [6][7][8], through computer simulations [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], and theoretical investigations including the study of elastoplastic models and corresponding mean field theories [4,13,[27][28][29][30][31][32][33]. These investigations have largely focused on the response to uniform shear, but several investigations have explored yielding behaviour under cyclic deformation [11, 12, 19, 21, 23-26, 29, 31-35].…”

Mean field theory of yielding under oscillatory shear

“…In any case it would be interesting to perform a thorough analysis of Eq. (50) in the disordered HL model.…”

“…It will be interesting to study the model with the "correct" power law mechanical noise spectrum as arising from Eshelby events, going beyond the diffusive approximation following [50,51] . Another avenue for future research will be to include thermal activation over barriers (as in SGR [37], [29]) within the elastoplastic model, following [52].…”